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Convex implementation of the Holevo-Cramer-Rao bound.

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HCRB_SDP

Semidefinite program (SDP) implementation of the Holevo-Cramer-Rao bound.

Original Matlab implementation by @falbarelli, this is my python port

Paper with more details

HolPure uses simplifications available to pure state for calculation of the HCRB, where as HolSDP is for general states.

Both HolPure and HolSDP implement a 'naghol_sdp' function that takes

  • phi/rho: (for pure/general respectively), the final parameter encoded state
  • dphi: a vector of derivatives of the parameter encoded state wrt to each parameter
  • d: dimension of Hilbert space

optional args

  • solve (MOSEK, CVXOPT, SCS): selects the SDP solver to use (we tend to use MOSEK for pure state and SCS for general)
  • verbose_state (bool): turn verbose messaging from the solver on/off

TODO

  1. Tidy up matlab implementation (mainly just removing the libraries I accidentally dumped into the repo, in a branch)
  2. Tighten up tests and add back into repo
  3. Code review (I know I need to make the imports explicit, comments for example)
  4. Improve this readme!
  5. Add examples of use in

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Convex implementation of the Holevo-Cramer-Rao bound.

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